Using a Parallelogram to find the Area of a Triangle

Date: 06/26/2001 at 18:58:46
From: Christy V.
Subject: Math/area
What is the area of a triangle with a height of 12 inches and a base
of 3 inches?
I tried it myself, but I just don't get it.

Date: 06/27/2001 at 17:12:03
From: Doctor Ian
Subject: Re: Math/area
Hi Christy,
Here's a way that you can figure this out when you've forgotten the
formula.
First, draw the triangle.
.
. . |
. . | 12
. . |
......... |
3
Now draw a mirror image of the triangle, reflected across one side:
.........
. . . |
. . . | 12
. . . |
......... |
3
Now you have a parallelogram, so the area of the triangle must be
exactly half the area of this parallelogram.
But what is the area of a parallelogram? Well, we can do a similar
trick for any parallelogram:
_____________
| / . /
| / . / <-- cut this part off, and move it ___
|/_________/ |
|
^ |
|_________________ here ______________________________|
So the area of any parallelogram is the same as the area of the
rectangle with the same base and height. But the area of a rectangle
is just the base times the height - so that means
area(triangle) = (1/2) * area(parallelogram)
= (1/2) * area(rectangle)
= (1/2) * base * height
Does this help? Write back if you'd like to talk about this some
more, or if you have any other questions.
- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/